big idea #3

Big Idea #3

Develop an understanding of operations of all rational numbers

and solving linear equations

Benchmarks » MA.7.A.3.1: Use and justify the rules for adding, subtracting, multiplying, dividing, and finding the absolute value of integers.

Depth of Knowledge: Moderate Date Adopted or Revised: 09/07

» MA.7.A.3.2: Add, subtract, multiply, and divide integers, fractions, and terminating decimals, and perform exponential operations with rational bases and whole number exponents including solving problems in everyday contexts.

Depth of Knowledge: Moderate Date Adopted or Revised: 09/07

» MA.7.A.3.3: Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational coefficients.

Depth of Knowledge: Moderate Date Adopted or Revised: 09/07

» MA.7.A.3.4: Use the properties of equality to represent an equation in a different way and to show that two equations are equivalent in a given context.

Depth of Knowledge: Moderate Date Adopted or Revised: 09/07

Thesis Statement

http://www.neirtec.org/activities/applets/numberline.htm

The purpose of this lesson is to work on Big Idea #3 from the 7th grade Next Generation Sunshine State Standards (NGSSS).It says,

MA.7.A.3.1: Use and justify the rules for adding, subtracting, multiplying, dividing, and finding the absolute value of integers.

This lesson will be divided into 3 parts

How we’ve been taught and How we are teaching. (2 Hours)

Hands-on Math and the CRA Sequence of Instruction (2 Hours)

A Process Does not Always Tell Us Why. (2 Hours)

Why Do I Need to Know This?(Motivation and Real World Applications)

http://www.labsafety.com/images/xl/Weather-Thermometer-40-to-LSS_i_LBM37561Z.jpg

In Chemistry

Protons – positive charge  

neutrons – neutral charge 

. 

electrons – negative charge

For example:

The World’s Tallest Building

H

http://img.dailymail.co.uk/i/pix/2007/07_02/WorldsTallestDM_468x525.jpg

Above and Below Sea Level

http://www.treehugger.com/mariana%20trench.jpghttp://www.thetravelpeach.com/asia-vacations/everest-mount.jpg

Mariana Trent-10,916

Mount Everest29,035

The U.S. National Debt

U.S. NATIONAL DEBT CLOCK The Outstanding Public Debt as of 09 Jan 2010 at 01:30:59 PM GMT

is:

http://www.brillig.com/debt_clock/

Floors on Elevators

An elevator panel with NEGATIVE numbers.

Vocabulary Words That You Need to Know

Addends, Sum, Minuend, Subtrahend, Difference, Factors, Products, Divisor, Dividend, Quotient, Mixed/Multiple Signs

Teaching Using Direction

What is -2 + 4?

Start Here

4

The Answer is 2.

What is -2 + 2?

Start Here

2

The Answer is 0.

What is -1 - 2?

Start Here

2

The Answer is -3.

What is +5 + 4?

Start Here

The Answer is 9.

…

What do you think?

Adding Using Mixed/Multple

Signs

Mixed/Multiple Signs

Mixed/Multiple Signs exist when two signs are together.

An addition and a positive ++An addition and a negative +-A subtraction and a positive - + A subtraction and a negative - -

These problems are not difficult, they just need to be solved a little differently.

What is +2 + -4?

Start Here

4

The Answer is -2.

What is -5 + +1?

Start Here

1

The Answer is -4.

What is -3 + -4?

Start Here

4

The Answer is -7.

…

What do you think?

What is +4 + +2?

Start Here

2

The Answer is 6.I bet you know this one.

Principles/Hypothesis Formed

1. When adding two integers and the signs are alike, you add and keep the sign.

2. When adding two integers and the signs are not alike, you subtract and take the largest numbers absolute value.

Subtracting Using Mixed/Multple

Signs

Principle

When subtracting two integers, you keep the minuend, change the subtraction symbol to an addition symbol, and change the sign of the subtrahend to its opposite.

KeepChange Change

What is -2 - -7?

Start Here

7

The Answer is 5.

Keep -2 Change to addition

Take the opposite of -7

What is -2 + +7?

What is 5 - 7?

The Answer is -2.

Keep 5 Change to addition

Take the opposite of 7

What is 5 + -7?

Principle: When adding two integers, and the signs are not alike, you subtract and take the sign of the largest numbers absolute value.

What is 3 - -9?

The Answer is 12.

Keep 3 Change to addition

Take the opposite of -9

What is 3 + 9 ?

Principle: When adding two integers, and the signs are the same, you add and keep the sign.

What is -5 - - 4?

The Answer is -1.

Keep -5 Change to addition

Take the opposite of -4

What is -5 + 4?

Principle: When adding two integers, and the signs are not alike, you subtract and take the sign of the largest numbers absolute value.

Multiplying Integers

Principle

1. When multiplying two integers and the signs are alike, the product is positive.

(+)(+) = (+) (-)(-) = (+)

2. When multiplying two integers and the signs are not alike, the product is negative.

(+)(-) = (-) (-)(+) = (-)

Why does a positive times a negative equal a negative?

4 • 3 = 124 • 2 = 8 4 • 1 = 44 • 0 = 0

4 • -1 = ?Look at th

e patternThe Answer is -4.

So a positive times a negative is a negative.

But why does a negative times a negative equal a positive?

-4 • 3 = -12-4 • 2 = -8 -4 • 1 = -4-4 • 0 = 0

-4 • -1 = ?Look at the pattern

The Answer is 4.

So a negative times a negative is a positive.

Well, knowing a positive times a negative is a negative, also means that a negative times a positive is a negative, so again…

Dividing Integers

Principle

1. When multiplying two integers and the signs are alike, the product is positive.

(+)/(+) = (+) (-)/(-) = (+)

2. When multiplying two integers and the signs are not alike, the product is negative.

(+)/(-) = (-) (-)/(+) = (-)

Bring it All Together

Floors on ElevatorsThis is an elevator panel with NEGATIVE numbers.

How far many floors have you gone up if you start at the lowest floor and go to the highest floor?

(1)Set up the expression(2)Explain your reasoning(3)Solve the problem

Answer: 17-(-2) = 19 floors

The World’s Tallest Building

http://img.dailymail.co.uk/i/pix/2007/07_02/WorldsTallestDM_468x525.jpg

How much taller is The Burj Dubai compared to The Empire State Building?

Answer: 512 – 381 = 131 meters

The U.S. National Debt

U.S. NATIONAL DEBT CLOCK The Outstanding Public Debt as of 09 Jan 2010 at 01:30:59 PM GMT

is:

http://www.brillig.com/debt_clock/

If the government taxed each American $40, 068.00, approximately how many Americans would it require to pay to off our National Debt?

Answer: -12,287,322,881,897 ÷ -40,068.00 ≈ 306,666,778 Americans

Why Do I Need to Know This?(Motivation and Real World Applications)

http://www.labsafety.com/images/xl/Weather-Thermometer-40-to-LSS_i_LBM37561Z.jpg

What is the difference between the lowest and the highest temperature reading on the thermometer?

Answer: 120 – (-40) = 160°F

Above and Below Sea Level

http://www.treehugger.com/mariana%20trench.jpg

http://www.thetravelpeach.com/asia-vacations/everest-mount.jpg

Mariana Trent-10,916

Mount Everest29,035

What is the difference between the highest point above sea level and the lowest point below sea level?

Answer: 29,035 – (-10,916) = 39,951